# Which test should I use to compare the means of two factors (motivations), which were surveyed at one time, of one sample?

I conducted the Academic Motivation Scale. This instrument returned three types of motivations, namely extrinsic, intrinsic and amotivation. The latter motivations means the absence of motivation towards cetain activity. In other words, no motivation. The descriptive analysis shows that mean of extrinsic motivation (M = 5.15, SD = 1.13) is higher than the mean of intrinsic motivation (M = 4.72, SD = 1.31). In this regard, my research question is "What is the statistically predominant type of motivation among graduate students to pursue master's degree?

Which test should I use to compare the means of these two motivation to examine possible difference? I quess that I could use paired sample t-test. However, from what I have read, this test compare means when the data collected in two times, before and after. In my case, I surveyed my sample at one time.

t-test should do your job. As a driver for further education, external motivation has a mean $\bar x_{extrinsic} = 5.15$ and internal motivation $\bar x_{intrinsic} = 4.72$. Findings from your sample indicates that students pursue master's degree motivated more extrinsically than intrinsically. Given the sample findings, you can test the hypothesis ($H_0: \mu_{extrinsic} \leq \mu_{intrinsic}$ ; $H_a: \mu_{extrinsic} \gt \mu_{intrisic}$) if the findings are significant for the entire population (all students pursuing master's are motivated more by extrinsic factors than intrinsic ones). Note that one-tailed t-test needs to be used because you are interested in whether one mean is larger than the other, not just in whether they are unequal.
Consider the following t-test assumptions and investigate if your sample holds.

• Continuous variable, i.e., extrinsic and intrinsic scores are measured as quantitative variable
• Each observation is independent of other observations
• Variable has a normal distribution (plot histogram of extrinsic scores and intrinsic scores to see if the distribution is normal)
• Should there be a consideration of the assumptions around the $t$-test? Normality should be checked. Additionally, was there an a priori belief that extrinsic factors should be less than intrinsic factors? If not and you're basing that null hypothesis after seeing the means in the data, I believe you're being disingenuous to the Type I error rate. Lastly, if there is justification for the 1-sided test, rejecting the null doesn't mean all students pursuing MS are motivated more by extrinsic factors; one can conclude with 95% confidence that the means are different. – Ashe Jun 8 '16 at 13:43
• I'm still concerned about my second two points. In particular with the 3rd, a significant $t$-test doesn't imply that all students pursuing MS are motivated more by intrinsic factors. It implies (with X% confidence) that for the typical student, they are more motivated by extrinsic factors. The other point, regarding the use of a 1-sided test, seems more motivated by looking at the data than having a predefined null hypothesis. If that's the case, it seems like playing with the Type I error rate to improve the significance. A 2-sided test seems much more appropriate here. – Ashe Jun 8 '16 at 14:07